Find each product. See Example 5.

(4r - 1) (7r + 2)

Question

Find each product. See Example 5.

(4r - 1) (7r + 2)

Accepted Answer

Hello, everyone. We are asked to perform the indicated operation to simplify the polynomial expression, open parentheses, five T minus four, closed parentheses multiplied by the parentheses. Eight T plus three. Our answer choices are a 40 T squared plus 47 T plus 12 B 40 T squared plus 17 T minus C 40 T squared minus 47 T plus 12 D 40 T squared minus T minus 12. Looking at my expression, I again, notice I have two binomials. So I have five T minus four and one set of parentheses and eight plus three in the next. And I recall that when I multiply binomials, I use what we call the foil method. So this is the order I'm going to multiply in F stands for first. So I'm gonna start by multiplying the first terms in the parentheses together. So that will be five T multiplied by eight T five, multiplied by eight is 40 T multiplied by T is T squared. So that's the F in foil O stands for outer. So this will be the outer elements of our binomials. So five T multiplied by three, five, multiplied by three is 15 and it's positive. So I'm right, plus 15 T will not change. So this is plus 15 T and that's our O in foil I stands for inner. So our inner two elements will be negative four multiplied by eight T. So negative four multiplied by eight is negative 32 and the T will not change. It's just going along with it. So we write down minus 32. That's our I and L stands for the last term. So the last term in each binomial, so negative four will be multiplied by three. So negative four, multiplied by three is negative 12. So minus 12. So at this step, we have 40 T squared plus 15 T minus T minus 12, we need to combine our like terms. So the only like terms we have here are our T terms. So 40 T squared stays, we're combining 15 T and negative 32 T which would be negative 17 T and then minus 12 because there's nothing to change that one. So 40 T squared minus 17 T minus 12 is our answer and it's answer choice. D have a nice day.

Find each product. See Example 5. (4r - 1) (7r + 2)

Key Concepts

Distributive Property

Combining Like Terms

Polynomial Multiplication

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